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Keywords:
averaged regression quantile; one-step regression quantile; $R$-estimator; functionals of the quantile process
Summary:
We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g.\ for coherent risk measures of various types in the situations with covariates.
References:
[1] G. W. Bassett, Jr.: A property of the observations fit by the extreme regression quantiles. Comput. Stat. Data Anal. 6 (1988), 353-359. DOI 10.1016/0167-9473(88)90075-8 | MR 0947589 | Zbl 0726.62104
[2] G. W. Bassett, Jr., R. Koenker: An empirical quantile function for linear models with iid errors. J. Am. Stat. Assoc. 77 (1982), 405-415. DOI 10.2307/2287261 | MR 0664682 | Zbl 0493.62047
[3] Gutenbrunner, C., Jurečková, J.: Regression rank scores and regression quantiles. Ann. Stat. 20 (1992), 305-330. DOI 10.1214/aos/1176348524 | MR 1150346 | Zbl 0759.62015
[4] Hájek, J.: Extension of the Kolmogorov-Smirnov test to regression alternatives. Proceedings of the International Research Seminar L. LeCam University of California Press, Berkeley (1965), 45-60. DOI 10.1007/978-3-642-99884-3_6 | MR 0198622 | Zbl 0142.15802
[5] Jaeckel, L. A.: Estimating regression coefficients by minimizing the dispersion of the residuals. Ann. Math. Stat. 43 (1972), 1449-1458. DOI 10.1214/aoms/1177692377 | MR 0348930 | Zbl 0277.62049
[6] Jurečková, J.: Averaged extreme regression quantile. Extremes 19 (2016), 41-49. DOI 10.1007/s10687-015-0232-2 | MR 3454030 | Zbl 1382.60079
[7] Jurečková, J., Picek, J.: Two-step regression quantiles. Sankhy$\bar a$ 67 (2005), 227-252. MR 2208888 | Zbl 1193.62114
[8] Jurečková, J., Picek, J.: Averaged regression quantiles. Contemporary Developments in Statistical Theory S. Lahiri et al. Springer Proceedings in Mathematics and Statistics 68, Springer, Cham (2014), 203-216. DOI 10.1007/978-3-319-02651-0_12 | MR 3149923 | Zbl 06312425
[9] Jurečková, J., Picek, J., Schindler, M.: Robust Statistical Methods With R. CRC Press, Boca Raton (2019). DOI 10.1201/b21993 | MR 3967085 | Zbl 1411.62003
[10] Jurečková, J., Sen, P. K., Picek, J.: Methodology in Robust and Nonparametric Statistics. CRC Press, Boca Raton (2013). DOI 10.1201/b12681 | MR 2963549 | Zbl 1281.62127
[11] Kloke, J. D., McKean, J. W.: Rfit: Rank-based estimation for linear models. The R Journal 4 (2012), 57-64. DOI 10.32614/RJ-2012-014
[12] Koenker, R.: Quantile Regression. Econometric Society Monographs 38, Cambridge University Press, Cambridge (2005). DOI 10.1017/CBO9780511754098 | MR 2268657 | Zbl 1111.62037
[13] Koenker, R.: quantreg: Quantile Regression. R package version 5.51. Available at https://CRAN.R-project.org/package=quantreg
[14] R. Koenker, G. Bassett, Jr.: Regression quantiles. Econometrica 46 (1978), 33-50. DOI 10.2307/1913643 | MR 0474644 | Zbl 0373.62038
[15] Portnoy, S.: Tightness of the sequence of empiric c.d.f. processes defined from regression fractiles. Robust and Nonlinear Time Series Analysis J. Franke et al. Lecture Notes in Statistics 26, Springer, New York (1984), 231-245. DOI 10.1007/978-1-4615-7821-5_13 | MR 0786311 | Zbl 0568.62065
[16] Portnoy, S.: Asymptotic behavior of the number of regression quantile breakpoints. SIAM J. Sci. Stat. Comput. 12 (1991), 867-883. DOI 10.1137/0912047 | MR 1102413 | Zbl 0736.62061
[17] Ruppert, D., Carroll, R. J.: Trimmed least squares estimation in the linear model. J. Am. Stat. Assoc. 75 (1980), 828-838. DOI 10.2307/2287169 | MR 0600964 | Zbl 0459.62055
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